Finite Group Databasebeta

← Prev (#31773152) Next (#31773154) →

C7×C11×C52⋊C9 #31773153

order17325
isoclinismisoclinic class of C52⋊C3
automorphism?
homologyAbelianization (H1) = C7×C9×C11 · Schur multiplier (H2) = C5

Aliases

direct productC7×C11×C52⋊C9
unambiguous semidirect productC52⋊(C7×C9×C11)
unambiguous semidirect product(C52×C11)⋊(C7×C9)

Splittings

derived, SylowC52 ⋊ C7×C9×C11
HallC52×C7×C11 ⋊ C9
HallC52×C11 ⋊ C7×C9
HallC52×C7 ⋊ C9×C11

Subgroups

subgroupG/H
center, hypercenterC3×C7×C11C52⋊C3
commutator, hypocenterC52C7×C9×C11
FrattiniC3C7×C11×C52⋊C3
Fitting, socle, prime radicalC3×C52×C7×C11C3
cosocleC3×C52C3×C7×C11
LCSG ▷ C52
UCSC1 ◁ C3×C7×C11

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3465

Conjugacy classes & character table

2541 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofC7⋊(C11⋊#90646)
maximal subgroup ofC7×C11×#90646, C7×C11⋊#90646, C11×C7⋊#90646, …
maximal normal subgroup ofC7×C11×#90646, C7×C11⋊#90646, C11×C7⋊#90646, …
maximal quotient ofC2×C7×C11×C52⋊C9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17325, 13);